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ON A CLASS OF SUPERSOLUBLE GROUPS

Published online by Cambridge University Press:  23 May 2014

A. BALLESTER-BOLINCHES*
Affiliation:
Departament d’Àlgebra, Universitat de València, Dr. Moliner, 50, 46100 Burjassot, València, Spain email Adolfo.Ballester@uv.es
J. C. BEIDLEMAN
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, USA email clark@ms.uky.edu
R. ESTEBAN-ROMERO
Affiliation:
Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Camí de Vera, s/n, 46022 València, Spain email resteban@mat.upv.es
M. F. RAGLAND
Affiliation:
Department of Mathematics, Auburn University at Montgomery, PO Box 244023, Montgomery, AL 36124-4023, USA email mragland@aum.edu
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Abstract

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A subgroup $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H$ of a finite group $G$ is said to be S-semipermutable in $G$ if $H$ permutes with every Sylow $q$-subgroup of $G$ for all primes $q$ not dividing $|H |$. A finite group $G$ is an MS-group if the maximal subgroups of all the Sylow subgroups of $G$ are S-semipermutable in $G$. The aim of the present paper is to characterise the finite MS-groups.

Type
Research Article
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

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